Forces in Two Dimensions - Mission F2D5 Detailed Help

An object of mass 'm' is resting upon an inclined plane with an incline angle of 'theta.' The coefficient of friction between the object and the plane is 'mu.' The object is at rest upon the incline. The free-body diagram is shown with the weight vector resolved into parallel and perpendicular components. Which of the following mathematical statements are correct?


 
Newton's Laws of Motion:
If an object is at rest and staying at rest, then the individual forces that act upon it must be balanced.


 
When analyzing an inclined plane situation, the gravity force is resolved into two components. One component is directed parallel to the plane and the other component is directed perpendicular to the plane. This has been done for you on the diagram. Once done, the gravity force can be ignored because it has been replaced by its two components. The remaining four forces can be compared. The two forces perpendicular to the inclined surface (Fnorm and Fperpendicular) will balance each other. If there is no acceleration, then the net force will be 0 N and the two forces parallel to the inclined surface (Fparallel and Ffriction) will also balance each other.


 
The force of friction (Ffrict) experienced by an object is often calculated using the equation: 
 
Ffrict= mu • Fnorm

where mu is the coefficient of friction (dependent predominantly upon the nature of the two surfaces that are in contact) and Fnorm is the normal force.

​For a static situation (the object is at rest), the static friction force can be less than or equal to mu•Fnorm. Static friction applies an amount of force equal to any accelerating force but eventually reaches its upper limit as more and more accelerating force is applied. When the upper limit is reached, the object budges from its at-rest-state and begins accelerating. It is at this moment that kinetic or sliding friction is the opposing force.


 

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